反射扩散过程的某些极限定理

设（Ｘｉ）是由如下随机微分方程所决定的反射扩散过程： Ｘｔ＝Ｘ０＋∫＾ｔ０σ（Ｘｓ）ｄＷｓ＋∫＾ｔ０ｂ（Ｘｓ）ｄｓ＋Ｌｔ－Ｕｔ， Ｌｔ＝∫＾ｔ０Ｉ｛０｝（Ｘｓ）ｄＬｓ，Ｕｔ＝∫＾ｔ０Ｉ｛１｝（Ｘｓ）ｄＵｓ。 本文证明了当ｔ→∞时，Ｐｘ｛Ｘｔ∈Ａ｝→π（Ａ），１／ｔＥｘ（Ｌｒ）→ａ，１／ｔ     

纯生过程的变异性

设｛Ｘ（ｔ）：ｔ≥０｝为零初值纯生过程，出生率为λｎｎ≥０，在本文中，我们证明了Ｆａｄｄｙ［７］的一个猜测：当生率为单调增加序列λ０≤λ１≤λ２≤…时，Ｖａｒ｛Ｘ（ｔ）｝≥Ｅ｛Ｘ（ｔ）｝；当出生率为单调减少序列时，Ｖａｒ｛Ｘ（ｔ）≤Ｅ｛Ｘ（ｔ）｝。     

稳定分量过程象集的一致测试和一致维数

令Ｘ（ｔ）＝Ｘ１（ｔ），…，ＸＮ（ｔ）为－ｄ维过程，其中Ｘｉ（ｔ）为ａｉ－阶ｄｉ－维稳定过程，设０＜ａｎ＜…＜ａ１≤２，ｄ＝ｄ１＋…＿ｄＮ。本文中，我们获得了当ａ１≤ｄ１时稳定分量过程Ｘ（ｔ）关于Ｂｏｒｅｌ集Ｅ的象Ｘ（Ｅ）的Ｈａｕｓｄｏｒｆｆ测度和Ｐａｃｋｉｎｇ测度的致上界和一致下界，当ａ１＞ｄ１时得到了相应测度的一个一致上界。同时我们给出了一致维数结果。     

两指标随机积分方程解的唯一性

在正交增量的随机积分基础上，利用Ｌｉｐｓｃｈｉｔｚ条件，讨论了下面一类两参数随机积分方程解的唯一性。Ｘ（ｓ，ｔ）＝Ｚ（ｓ，０）＋Ｚ（０，ｔ）－Ｚ（０，０）＋∫Ｒｓｔα（ｕ，ｖ，Ｘ）ｄＭｕｖ＋∫Ｒｓｔβ（ｕ，ｖ，Ｘ）ｄｍｕｖ＋∫Ｒ＾ｓｔγ１（ｕ，ｖ，ｕ＇，ｖ＇，Ｘ）ｄＭｕｖｄＭｕ＇ｖ＇＋∫Ｒ＾２ｓｔγ２（ｕ，ｖ，ｕ＇，ｖ＇，Ｘ）ｄＭｕｖｄｍｕ＇ｖ＇＋∫Ｒ＾２ｓｔγ３（ｕ，ｖ，ｕ＇，ｖ＇，Ｘ）ｄｍｕｖ     

局部平方可积鞅的Chug重对数律

设Ｘ＝（Ｘｔ，ｔ≥０）为局部平方可积鞅，且Ｘ０＝０〈Ｘ，Ｘ〉ｔ为其二阶可料变差。利用继续半鞅的强逼近结果，我们证明了在较弱的条件下，Ｘ的Ｃｈｕｎｇ重对数律成立，即ｐ（＾ｌｉｍｉｎｆ ｔ→∞ ＾ｓｕｐ│Ｘｓ│ ｏ≤ｓ≤ｔ／（〈ｘ，ｘ〉ｔ／ｌｏｇｌｏｇ〈Ｘ，Ｘ〉 ｔ）＾１／２＝π／根号８）＝１。     

非时齐Poisson过程MLE的重对数律

在时间区间（０，Ｔ）上，我们观察到Ｘ（Ｔ）＝（Ｘ（ｔ，θ）０≤ｔ≤Ｔ），其中θ∈⊙为参数，且未知，Ｋｕｔｏｙａｎｔｓ讨论了非时齐过程参数θ的最大似然估计（ＭＬＥ）的性质，他给出了极限分布，并且得到了弱收敛及矩收敛等结果，但他要求参数空间为有限区间（α，β）。本文讨论了非时齐Ｐｏｉｓｓｏｎ过程ＭＬＥ的性质，我们允许参数空间随时间而不渐增大，即θｔ是θ在Ｔ＝（α，βＴ）上的最大似然估计，其中ｌｉｍβＴ     

协方差函数可微的高斯过程之极值逗留

设（Ｘ（ｔ），Ｔ１≤ｔ≤Ｔ２）是可分，可测的高斯过程，均值函数为零，而协方差函数Г（ｓ，ｔ）＝ＥＸ（ｓ）Ｘ（ｔ）具有连续一阶偏导，对于水平ｕ↑∞，本文讨论Ｘ（ｔ）在ｕ上的逗留极限定理。     

奇异半线性发展方程的局部Cauchy问题

本文在Ｂａｎａｃｈ空间Ｅ中讨论如下问题ｄｕｄｔ＋１ｔσＡｕ＝Ｊ（ｕ），０＜ｔＴ，ｌｉｍｔ→０＋ｕ（ｔ）＝０，其中ｕ：（０，Ｔ］Ｅ，Ａ是与ｔ无关的线性算子．（－Ａ）是Ｅ上Ｃ０半群｛Ｔ（ｔ）｝ｔ０的无穷小生成元，常数σ１，Ｊ是一个非线性映射ＥＪ→Ｅ．它满足局部Ｌｉｐｓｃｈｉｔｚ条件．我们证明了当其Ｌｉｐｓｃｈｉｔｚ常数ｌ（ｒ）满足一定条件时．问题（Ｓ）有局部解，且在某函类中解唯一．设Ｊ（ｕ）＝｜ｕ｜γ－１ｕ＋ｆ（ｘ）（γ＞１），Ｅ＝Ｌｐ，ＥＪ＝Ｌｐγ时得到了与Ｗｅｉｓｌｅｒ［２］在非奇异情形类似的结果．     

Global Asymptotic Stability for a Class of Nonlinear Populations Model

Ｉｎａｎａｇｅｓｔｒｕｃｔｕｒｅｄｐｏｐｕｌａｔｉｏｎｍｏｄｅｌ,ｔｈｅｆｉｓｈｅｓｓｙｓｔｅｍｏｆａｆｉｓｈｇｒｏｕｎｄｃａｎｂｅｄｅｓｃｒｉｂｅｄａｓｆｏｌｌｏｗｉｎｇｍｏｄｅｌ：ｕ（ａ,ｔ）ｔ＋ｕ（ａ,ｔ）ａ＝－μ（ａ）ｕ（ａ,ｔ）,　０ａＡ,ｔ０,ｕ（ａ,０）＝ｕ０（ａ）,ｕ（０,ｔ）＝ｆ［Ｅ（ｔ）］Ｅ（ｔ）,Ｅ（ｔ）＝∫Ａ０ｂ（ａ）ｕ（ａ,ｔ）ｄａ．（１）Ｗｈｅｒｅｕ（ａ,ｔ）ｄｅｎｏｔｅｓａｇｅｄｉｓｔｒｉｂｕｔｉｖｅｄｅｎｓｉｔｙｆｕｎｃｔｉｏｎｏｆｆｉｓｈｅｄａｔｔ…     

A STRASSEN LAW OF THE ITERATED LOGARITHM FOR PROCESSES WITH INDEPENDENT INCREMENT

ＡＳＴＲＡＳＳＥＮＬＡＷＯＦＴＨＥＩＴＥＲＡＴＥＤＬＯＧＡＲＩＴＨＭＦＯＲＰＲＯＣＥＳＳＥＳＷＩＴＨＩＮＤＥＰＥＮＤＥＮＴＩＮＣＲＥＭＥＮＴＷａｎｇＪｉａｇａｎｇＡｂｓｔｒａｃｔＬｅｔＸ＝｛Ｘ（ｔ），ｔ０｝ｂｅａｐｒｏｃｅｓｗｉｔｈｉｎｄｅｐ...     

Monoids for Which Condition (P) Acts are Projective

A characterisation of monoids for which all right S-acts satisfying conditions (P) are projective is given. We also give a new characterisation of those monoids for which all cyclic right S-acts satisfying condition (P) are projective, similar in nature to recent work by Kilp [6]. In addition we give a sufficient condition for all right S-acts that satisfy condition (P) to be strongly flat and show that the indecomposable acts that satisfy condition (P) are the locally cyclic acts.     

Kähler Metrics on the Projective Bundle of a Holomorphic Finsler Vector Bundle

Let (M, g) be a compact Kähler manifold and (E, F) be a holomorphic Finsler vector bundle of rank r ≥ 2 over M. In this paper, we prove that there exists a Kähler metric φ defined on the projective bundle P (E) of E, which comes naturally from g and F. Moreover, a necessary and sufficient condition for φ having positive scalar curvature is obtained, and a sufficient condition for φ having positive Ricci curvature is established.     

一个关于上凸密度猜测的否定回答

Let E be a self-similar set satisfying the open set condition. Professor Xu conjectures in his doctoral degree thesis that if H^8（E） 〈｜E｜^8, then for any x ∈ E, the inequality ^-D^3C（E,x）〉H^8（E）/｜E｜^8holds, where 3 = dimH（E）. The above conjecture is negatively answered in this＇paper.     

K(o)the-Bochner空间的凸性

本文利用K(o)the函数空间的性质以及K(o)the函数空间与K(o)the-Bochner空间的关系,讨论了K(o)the-Bochner空间E(X)的凸性,主要结果如下:(a)给出E(X)的端点的充分条件,得到了E(X)严格凸的判据,相应地推广了Lp(μ,X)以及LΦ(X)的结果;(b)讨论了E(X)的弱局部一致凸和局部完全k-凸;(c)刻画了E(X)的强凸,给出了E(X)强凸的充要条件.     

TOEPLITZ ALGEBRAS ON DISCRETE GROUPS AND THEIR NATURAL MORPHISMS

Let G be a discrete group, E1 and E2 be two subsets of G with E1(?)E2, and e ∈E2. Denote by TE1 and TE2 the associated Toeplitz algebras. In this paper, it is proved that the natural morphism γE2,E1 from TE1 to TE2 exists as a C*-morphism if and only if E2 is finitely covariant-lifted by E1 Based on this necessary and sufficient condition, some applications are made.     

关于U-统计量完全收敛性

本文讨论了满足E[f(xi,yj)xi]=E[f(xi,yj)xj]=0的U－统计量最大值完全收敛性的充分条件,降低了王岳宝1996年论文中的矩条件,进一步对一般形式的多元函数的U－统计量最大值的完全收敛性的充分条件进行了讨论,得到了较理想的结果。     

Beck, H and Leech Coextensions

J. Leech studied certain coextensions ES , of a monoid S and Ch. Wells studied the relationship between Leech coextensions and those studied in a general categorical setting by J. Beck. In this paper it is completed some of the Wells results and it is given a classification of the Leech coextensions. Specifically, Wells shows that a Leech coextension is a Beck coextension if its corresponding functor is "centralizing" (a generalization of abelian-valued). Our Theorem 1.1 provides a technical condition under which Beck coextensions are actually abelian. This technical condition implies other properties as well. Corollary 1.8 provides three natural conditions under any of which the conditions of 1.1 are satisfied. Also it is provided an example of a non-abelian Beck coextension. Table 1 shows the general classification and Table 2 shows the reduced set of possibilities when the semigroup is a regular monoid. Stronger results are provided for coextensions with S an inverse monoid, and for extensions of groups by monoids.     

初等算子的正规性

设初等算子E（X）＝n↑∑↑i=1AiXBi，定义E^*(X)=n↑∑↑i=1Ai^*XBi^*我们证明了EE^*＝E^*E当县仅当｛Ai｝和｛Bi｝都是交换的正规算子族，从而回答了由D.Keckic提出的关于初等算子正规性的开问题。我们还给出了E＝E^*的充分必要条件。     

单调及保凸二次样条插值

本文将集中研究保形二次样条插值.假设序列X={x_i}和Y={y_i}(i=0,1,2,…,N)满足x_(i-1)相似文献   

On the Existence of Suprema of Infinite Many Elements in a Riesz Space

<正> Let E be a Riesz space with a disjoint system {u_i :i∈I}. We denote by E_i the principal band generated by u_i(i∈I). A necessary and sufficient condition is found in this paper under which sup{X_i:i∈I} exists in E for every x_i∈E (i∈I).